What Are Your Chances of a Profitable Match at Keno?

It's tough to deny the appeal of propositions proffering big bucks for itty-bitty bets. Slot machines and jackpot side-bets in Caribbean Stud are like that. But most such games aren't designed for taking a quick shot and walking away. They're meant to be played for extended sessions. So, chump change nobody will lament losing can quickly become major money mournfully missed.

Keno - live as opposed to the slot machine version - is different. Solid citizens make their bets then typically engage in other endeavors and get the news later. Other than an occasional keno crackpot, even fervid fans of this activity only enter a few games during the course of a casino visit.

You probably know how keno works. The field has 80 numbers. You choose from one to 15 spots. A random process - it used to be lotto-like balls blown about by air blasts, now it's often a computer - "draws" 20 numbers. Whether and how much you win depend on how many of your choices match those drawn by the house.

For a mammoth payoff, you've got to pick a large set of numbers and match a lot of them. If you choose a big bunch and hit half or so, you may win a little. Starting with a small set, you may grab up to ten, a hundred, maybe a thousand times your bet - but you can't get that limo ride to Easy Street even if they all pop.

The key is the probability, or chance, of various matches. The lower the likelihood of an event, the more you collect if it occurs. Unsophisticated players look only at the rich rewards on the right-hand side of the roster and haven't a clue as to the prospects of collecting.

The accompanying table gives the probability of hitting from none to all of your spots for sets of one to 15 numbers. In the table, all those "<0.1%" entries mean "less than one tenth of a percent," and "*0.1%" means "much less than one tenth of a percent."

Here are a few examples showing how to interpret the table.
o Suppose you pick five numbers. You've got a 22.7 percent chance none will hit, an 8.4 percent chance three will hit, down to a 0.1 percent chance all five will hit.
o Maybe you've a hunch you'll win with 10 numbers. The probability of a single match is 18.0 percent, of five matches is 5.1 percent, and of eight matches is less than 0.1 percent. Notice you're more apt to make no matches whatsoever (probability is 4.6 percent) than of matching six or more of the drawn numbers (combined probability is about 1.3 percent).

o Now say you go hog wild with 14 numbers. You've a 2.0 percent chance half will hit, 0.4 percent chance eight will hit, and much less than 0.1 percent chance of a grand slam; it's not given, but the actual probability of 14 matches is 0.00000000257 percent - one chance out of 389 million.

There's no right or wrong strategy for keno. No matter how you play, the chances of a win are low and the house edge is usurious. And "systems" like picking patterns of numbers or selecting sectors of the card are humbug.

Bear in mind, however, why any quasi-cognitive adult would consider coughing-up the costly commission casinos claim on keno. It's the possibility - however remote - of a serious payoff for a trivial wager. On this basis, risking more than occasional mad money, or restricting yourself at best to a modest win by selecting only a limited set of numbers, more or less jades the joy of the affair. Sumner A Ingmark, poet with a punter's penchant for probability, put it perfectly:

Though there's high house edge, which we know,
Knocks a gambler down, I see no,
Cause to bar a shot at keno.

Table Probability of Various Numbers of Matches at Keno
	match 0	1	2	3	4	5	6	7	8	9	10	11 to 15
pick 1	75.0%	25.0%
2	56.0%	38.0%	6.0%
3	41.6%	43.1%	13.9%	1.4%
4	30.8%	43.3%	21.3%	4.3%	0.3%
5	22.7%	40.6%	27.0%	8.4%	1.2%	0.1%
6	16.7%	36.3%	30.8%	13.0%	2.9%	0.3%	<0.1%
7	12.1%	31.5%	32.7%	17.5%	5.2%	0.9%	0.1%	*0.1%
8	8.8%	26.6%	32.8%	21.5%	8.2%	1.8%	0.2%	<0.1%	*0.1%
9	6.4%	22.1%	31.6%	24.6%	11.4%	3.3%	0.6%	<0.1%	*0.1%	*0.1%
10	4.6%	18.0%	29.5%	26.7%	14.7%	5.1%	1.1%	0.2%	<0.1%	*0.1%	*0.1%
11	3.3%	14.4%	26.8%	27.8%	17.8%	7.4%	2.0%	0.4%	<0.1%	*0.1%	*0.1%	*0.1%
12	2.3%	11.4%	23.8%	28.0%	20.6%	9.9%	3.2%	0.7%	0.1%	*0.1%	*0.1%	*0.1%
13	1.6%	8.9%	20.7%	27.3%	22.7%	12.6%	4.8%	1.2%	0.2%	<0.1%	*0.1%	*0.1%
14	1.1%	6.8%	17.6%	25.9%	24.2%	15.2%	6.6%	2.0%	0.4%	<0.1%	*0.1%	*0.1%
15	0.8%	5.2%	14.8%	24.0%	25.0%	17.6%	8.7%	3.0%	0.7%	0.1%	<0.1%	*0.1%